Problem: Simplify the following expression: $a = \dfrac{6n^2 + 60n + 126}{n + 3} $
First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $6$ , so we can rewrite the expression: $ a =\dfrac{6(n^2 + 10n + 21)}{n + 3} $ Then we factor the remaining polynomial: $n^2 + {10}n + {21} $ ${3} + {7} = {10}$ ${3} \times {7} = {21}$ $ (n + {3}) (n + {7}) $ This gives us a factored expression: $\dfrac{6(n + {3}) (n + {7})}{n + 3}$ We can divide the numerator and denominator by $(n - 3)$ on condition that $n \neq -3$ Therefore $a = 6(n + 7); n \neq -3$